{
  "id": "2103.14164",
  "version": "v1",
  "published": "2021-03-25T22:39:35.000Z",
  "updated": "2021-03-25T22:39:35.000Z",
  "title": "On Donkin's Tilting Module Conjecture I: Lowering the Prime",
  "authors": [
    "Christopher P. Bendel",
    "Daniel K. Nakano",
    "Cornelius Pillen",
    "Paul Sobaje"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "In this paper the authors provide a complete answer to Donkin's Tilting Module Conjecture for all rank $2$ semisimple algebraic groups and $\\text{SL}_{4}(k)$ where $k$ is an algebraically closed field of characteristic $p>0$. In the process, new techniques are introduced involving the existence of $(p,r)$-filtrations, Lusztig's character formula, and the $G_{r}$T-radical series for baby Verma modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T22:39:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20J06"
    ],
    "keywords": [
      "donkins tilting module conjecture",
      "baby verma modules",
      "lusztigs character formula",
      "semisimple algebraic groups",
      "complete answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}